Lahenda frac{x^{2}}{x^{2}-y^2}-x/x+y+y/2x-2y-y^2/2x^2-2y^2

$$\frac { x ^ { 2 } } { x ^ { 2 } - y ^ { 2 } } - \frac { x } { x + y } + \frac { y } { 2 x - 2 y } - \frac { y ^ { 2 } } { 2 x ^ { 2 } - 2 y ^ { 2 } }$$

Arvuta

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$

Lühike lahenduskäik

Tegurda x^{2}-y^{2}.

$$\frac{x^{2}}{\left(x+y\right)\left(x-y\right)}-\frac{x}{x+y}+\frac{y}{2x-2y}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x+y\right)\left(x-y\right) ja x+y vähim ühiskordne on \left(x+y\right)\left(x-y\right). Korrutage omavahel \frac{x}{x+y} ja \frac{x-y}{x-y}.

$$\frac{x^{2}}{\left(x+y\right)\left(x-y\right)}-\frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}+\frac{y}{2x-2y}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Kuna murdudel \frac{x^{2}}{\left(x+y\right)\left(x-y\right)} ja \frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} on sama nimetaja, lahutage nende lugejad.

$$\frac{x^{2}-x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}+\frac{y}{2x-2y}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Tehke korrutustehted võrrandis x^{2}-x\left(x-y\right).

$$\frac{x^{2}-x^{2}+xy}{\left(x+y\right)\left(x-y\right)}+\frac{y}{2x-2y}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Kombineerige sarnased liikmed avaldises x^{2}-x^{2}+xy.

$$\frac{xy}{\left(x+y\right)\left(x-y\right)}+\frac{y}{2x-2y}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Tegurda 2x-2y.

$$\frac{xy}{\left(x+y\right)\left(x-y\right)}+\frac{y}{2\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. \left(x+y\right)\left(x-y\right) ja 2\left(x-y\right) vähim ühiskordne on 2\left(x+y\right)\left(x-y\right). Korrutage omavahel \frac{xy}{\left(x+y\right)\left(x-y\right)} ja \frac{2}{2}. Korrutage omavahel \frac{y}{2\left(x-y\right)} ja \frac{x+y}{x+y}.

$$\frac{2xy}{2\left(x+y\right)\left(x-y\right)}+\frac{y\left(x+y\right)}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Kuna murdudel \frac{2xy}{2\left(x+y\right)\left(x-y\right)} ja \frac{y\left(x+y\right)}{2\left(x+y\right)\left(x-y\right)} on sama nimetaja, liitke nende lugejad.

$$\frac{2xy+y\left(x+y\right)}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Tehke korrutustehted võrrandis 2xy+y\left(x+y\right).

$$\frac{2xy+xy+y^{2}}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Kombineerige sarnased liikmed avaldises 2xy+xy+y^{2}.

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

Tegurda 2x^{2}-2y^{2}.

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

Kuna murdudel \frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)} ja \frac{y^{2}}{2\left(x+y\right)\left(x-y\right)} on sama nimetaja, lahutage nende lugejad.

$$\frac{y^{2}+3xy-y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

Kombineerige sarnased liikmed avaldises y^{2}+3xy-y^{2}.

$$\frac{3xy}{2\left(x+y\right)\left(x-y\right)}$$

Laiendage 2\left(x+y\right)\left(x-y\right).

$$\frac{3xy}{2x^{2}-2y^{2}}$$

Lahuta teguriteks

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$